Spacecraft formation trajectory tracking distributed control method and related equipment

Abstract

The application provides a spacecraft formation trajectory tracking distributed control method and related equipment, comprising: constructing a relative motion PH equation of each spacecraft in a target spacecraft formation; converting the relative motion PH equation of each spacecraft respectively to obtain a relative motion trajectory tracking error PH equation of the target spacecraft as a tracking error system of the target spacecraft formation; based on the tracking error system, constructing an expected Hamilton function that couples the relative position error of each spacecraft in the target spacecraft formation to the tracking error system; designing a control law of the target spacecraft formation according to the expected Hamilton function and calculating a value of the distributed cooperative control law of the target spacecraft formation; performing trajectory tracking distributed control on the target spacecraft formation according to the value of the distributed cooperative control law; the spacecraft formation can accurately and quickly reach the expected motion trajectory and maintain the configuration, and the distributed cooperative control of the spacecraft cluster network is realized.

Description

Technical Field

[0001] This invention relates to the field of spacecraft formation trajectory tracking and control technology, and in particular to a distributed control method and related equipment for spacecraft formation trajectory tracking. Background Technology

[0002] Spacecraft formation refers to a cluster of spacecraft linked by a specific topology according to designated mission requirements. Through cooperation among the member spacecraft, it functions as a large "virtual spacecraft." During in-orbit flight, the formation's trajectory needs to be tracked and controlled to achieve different missions and reach a predetermined configuration. Currently, various control methods are applied to spacecraft formation control, such as nonlinear adaptive control, sliding mode methods, linear quadratic regulation, IDA-PBC (Interconnection and Damping Assignment Passivity-Based Control), impulse control, model predictive control, and fast search random trees. Formation cooperation methods mainly include leader-follower methods, virtual structure methods, and swarm control.

[0003] In recent years, Port-Hamiltonian (PH) system theory, which employs energy concepts, has gradually emerged and developed rapidly, providing a promising solution for modeling and controlling complex nonlinear systems. Furthermore, PH theory achieves system control from an energy perspective, solving the problem of selecting Lyapunov functions, and models built using it are more consistent with practical engineering applications. In the field of spacecraft formation control, the Port-Hamiltonian system method has been preliminarily studied. Chang Liu et al. transformed the circular restricted three-body problem into a Port-Hamiltonian system form, designed a control strategy based on energy shaping and damping injection, ensuring asymptotic stability and allowing arbitrary setting of equilibrium points. Ewoud Vos et al. established a two-dimensional two-body orbital dynamics model in the equatorial plane with a Port-Hamiltonian system, obtained the error system PH model relative to the target orbit using the generalized canonical transformation method, and then designed an internal control law based on virtual spring damping to guide each satellite to the target orbit, as well as a distributed relative motion control law based on virtual spring damping interaction to ensure that multiple satellites are evenly distributed in the orbit. This paper represents the first attempt at cooperative control of a multi-satellite port Hamiltonian system, targeting the position-keeping control problem of a special constellation; however, since spacecraft formation trajectory tracking is time-varying, and time-varying port Hamiltonian systems generally do not satisfy passivity.

[0004] IDA-PBC is a control law design method for nonlinear systems. Since its introduction by Ortega.R et al. in 2001, it has been applied to numerous fields, including spacecraft control. For example, Najmeh Javanmardi et al. designed a tracking control law using the IDA-PBC control method and compressed analysis. However, their method is based on a one-to-one leader / follower tracking mechanism, lacking coordination and feedback mechanisms. This research did not provide a solution for achieving distributed collaborative control in a clustered network. Summary of the Invention

[0005] This invention provides a distributed control method and related equipment for spacecraft formation trajectory tracking, the purpose of which is to realize distributed collaborative control of spacecraft clusters in a networked manner and reduce the relative distance error between spacecraft.

[0006] To achieve the above objectives, the present invention provides a distributed control method for spacecraft formation trajectory tracking, comprising:

[0007] Step 1: Construct the relative motion equations (PH) for each spacecraft in the target spacecraft formation; the relative motion equations (PH) are used to describe the relative motion trajectory of each spacecraft.

[0008] Step 2: Transform the relative motion equation PH for each spacecraft to obtain the relative motion trajectory tracking error equation PH for the target spacecraft formation. The relative motion trajectory tracking error equation PH serves as the tracking error system for the target spacecraft formation. The relative motion trajectory tracking error equation PH is used to describe the tracking error of the relative motion trajectory.

[0009] Step 3: Based on the tracking error system, construct the desired Hamiltonian function that couples the relative position error of each spacecraft in the target spacecraft formation to the tracking error system;

[0010] Step 4: Design the control law for the target spacecraft formation based on the desired Hamiltonian function, and substitute the actual state and desired state of the target spacecraft formation into the control law for calculation to obtain the value of the distributed cooperative control law for the target spacecraft formation.

[0011] Step 5: Perform distributed control for trajectory tracking of the target spacecraft formation based on the value of the distributed cooperative control law.

[0012] Furthermore, the relative motion equation PH for each spacecraft is:

[0013]

[0014]

[0015] in, Let x be the derivative of x, x be the spacecraft's velocity and acceleration, and J be the spacecraft's interconnect matrix. H(x,t) is the energy function, x is the state variable of the spacecraft, t is time, and G has no specific physical meaning. u is the input of the spacecraft, I is the identity matrix, and y is the output of the spacecraft.

[0016] Furthermore, the equation for the tracking error PH of the relative motion trajectory of the target spacecraft formation is:

[0017]

[0018]

[0019] in, For spacecraft velocity and acceleration errors, I n Let n be an n-order identity matrix, where n is the number of spacecraft. For the Kronecker product of matrices, For spacecraft interconnection matrix, Let Hamiltonian function be the tracking error system of a spacecraft formation, which consists of multiple spacecraft tracking error systems. For the formation tracking error system status, It is a coefficient matrix with no specific physical meaning. For formation error system output, This is the system control law.

[0020] Furthermore, the expected Hamiltonian function of the relative position error in the distributed topology is:

[0021]

[0022] Where n is the number of spacecraft, a ij For elements of the adjacency matrix, a ij ≠0, k p For interconnection coefficients, The error in maintaining the relative distance between spacecraft i and spacecraft j. x i Let be the error of the i-th spacecraft. Let be the error of the j-th spacecraft.

[0023] Furthermore, step 4 includes:

[0024] Based on the Hamiltonian function of the formation tracking error system, which consists of multiple spacecraft tracking error systems. We can obtain:

[0025]

[0026] in, Status of the target spacecraft formation tracking error system;

[0027] The expected Hamiltonian function of the relative position error in the distributed topology is:

[0028]

[0029] According to if The expected Hamiltonian function H in the system d (x), symmetric matrix R d (x)≥0 and antisymmetric matrix J d (x) satisfies the theorem for partial differential equations, and the matching equation can be solved as follows:

[0030]

[0031] in, L is the Laplace matrix, and A is the adjacency matrix. J 12 For the elements of matrix J,

[0032] according to and The arbitrariness of J satisfies the condition of this equation. 11 =R 11 J 12 =I3, can be set

[0033]

[0034]

[0035] According to If the system expects the Hamiltonian function H... d (x), symmetric matrix R d (x)≥0 and antisymmetric matrix J d Since (x) satisfies the theorem for partial differential equations, the control law of the system is:

[0036]

[0037] Will Substitution In the process, the distributed cooperative control law of the target spacecraft formation is obtained as follows:

[0038]

[0039] Where, k d is the damping coefficient.

[0040] Furthermore, based on the distributed cooperative control law of the target spacecraft formation, the control law of the i-th spacecraft in the tracking error system of the target spacecraft formation can be obtained as follows:

[0041]

[0042] Based on the control law of the i-th spacecraft in the tracking error system, the control law of the i-th spacecraft in the target spacecraft formation can be obtained as follows:

[0043]

[0044] in,

[0045] The present invention also provides a distributed control device for spacecraft formation trajectory tracking, comprising:

[0046] The module is used to construct the relative motion equations (PH) for each spacecraft in the target spacecraft formation; the relative motion equations (PH) are used to describe the relative motion trajectory of each spacecraft.

[0047] The conversion module is used to convert the relative motion equation PH for each spacecraft separately to obtain the relative motion trajectory tracking error equation PH for the target spacecraft formation, thus obtaining the tracking error system of the target spacecraft formation; the relative motion trajectory tracking error equation PH is used to describe the tracking error of the relative motion trajectory;

[0048] The construction module is used to construct the desired Hamiltonian function that couples the relative position error of each spacecraft in the target spacecraft formation to the tracking error system, based on the tracking error system.

[0049] The calculation module is used to design the control law of the target spacecraft formation based on the desired Hamiltonian function, and to calculate the value of the distributed cooperative control law of the target spacecraft formation by substituting the actual state and desired state of the target spacecraft formation into the control law.

[0050] The control module is used to perform distributed control for trajectory tracking of the target spacecraft formation based on the value of the distributed cooperative control law.

[0051] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements a distributed control method for spacecraft formation trajectory tracking.

[0052] The present invention also provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a distributed control method for spacecraft formation trajectory tracking.

[0053] The above-described solution of the present invention has the following beneficial effects:

[0054] This invention constructs relative motion equations (PH) for each spacecraft in a target spacecraft formation to describe the relative trajectory of each spacecraft. The relative motion equations (PH) for each spacecraft are then transformed to obtain the relative trajectory tracking error equations (PH) for the target spacecraft formation, resulting in a tracking error system for describing the tracking error of the relative trajectory. Based on the tracking error system, a desired Hamiltonian function is constructed that couples the relative position error of each spacecraft in the target spacecraft formation to the tracking error system. A control law for the target spacecraft formation is designed based on the desired Hamiltonian function, and the actual and desired states of the target spacecraft formation are substituted into the control law for calculation to obtain the value of the distributed cooperative control law for the target spacecraft formation. Distributed trajectory tracking control of the target spacecraft formation is then performed based on the value of the distributed cooperative control law. Under the action of the distributed cooperative control law designed in this invention, the spacecraft formation can accurately and quickly reach the desired trajectory and maintain its configuration, realizing distributed cooperative control of a networked spacecraft cluster. Compared with the independent following control law of the prior art, this method achieves higher configuration maintenance accuracy, faster convergence speed, smaller applied acceleration, and also reduces the relative distance error between spacecraft.

[0055] Other beneficial effects of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0056] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0057] Figure 2 This is a schematic diagram of the tracking trajectories of the first three spacecraft in the spacecraft formation in an embodiment of the present invention;

[0058] Figure 3 This is a graph showing the trajectory error versus time for the first three spacecraft in the spacecraft formation during independent control, as described in an embodiment of the present invention.

[0059] Figure 4 This is a graph showing the trajectory error versus time for the first three spacecraft in a spacecraft formation during distributed control in an embodiment of the present invention.

[0060] Figure 5 This is a graph showing the trajectory error versus time between adjacent spacecraft in the first three spacecraft of the spacecraft formation in an embodiment of the present invention when they are under independent control.

[0061] Figure 6 This is a graph showing the trajectory error versus time between adjacent spacecraft in the first three spacecraft of the spacecraft formation during distributed control in an embodiment of the present invention.

[0062] Figure 7 This is a graph showing the acceleration versus time applied to the first three spacecraft in a spacecraft formation during independent control in an embodiment of the present invention.

[0063] Figure 8 This is a graph showing the acceleration versus time applied to the first three spacecraft in a spacecraft formation during distributed control in an embodiment of the present invention. Detailed Implementation

[0064] To make the technical problems, solutions, and advantages of this invention clearer, a detailed description will be provided below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0065] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0066] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a locking connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0067] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0068] This invention addresses existing problems by providing a distributed control method and related equipment for spacecraft formation trajectory tracking.

[0069] like Figure 1 As shown, an embodiment of the present invention provides a distributed control method for spacecraft formation trajectory tracking, comprising:

[0070] Step 1: Construct the relative motion equations (PH) for each spacecraft in the target spacecraft formation; the relative motion equations (PH) are used to describe the relative motion trajectory of each spacecraft.

[0071] Step 2: Transform the relative motion equation PH for each spacecraft to obtain the relative motion trajectory tracking error equation PH for the target spacecraft formation, thus obtaining the tracking error system of the target spacecraft formation; the relative motion trajectory tracking error equation PH is used to describe the tracking error of the relative motion trajectory.

[0072] Step 3: Based on the tracking error system, construct the desired Hamiltonian function that couples the relative position error of each spacecraft in the target spacecraft formation to the tracking error system;

[0073] Step 4: Design the control law for the target spacecraft formation based on the desired Hamiltonian function, and substitute the actual state and desired state of the target spacecraft formation into the control law for calculation to obtain the value of the distributed cooperative control law for the target spacecraft formation.

[0074] Step 5: Perform distributed control for trajectory tracking of the target spacecraft formation based on the value of the distributed cooperative control law.

[0075] Specifically, the port Hamiltonian system of the spacecraft formation in this embodiment of the invention is as follows:

[0076]

[0077] in, Let x be the derivative of x, where x is the spacecraft velocity and acceleration, x is the system state variable, H(x,t) is the system Hamiltonian function, u is the system input, y is the system output, and J is an antisymmetric matrix, representing the system interconnection matrix. R is a non-negative definite symmetric matrix, which is the damping matrix of the system. I is the identity matrix, G = [0, ..., G] 3×3 I3] T ,

[0078] The definitions and theorems involved in the embodiments of this invention include:

[0079] Definition 1: If the transformation Convert the port Hamiltonian system (1) of the spacecraft formation into:

[0080]

[0081] This transformation is the generalized canonical transformation of the port Hamiltonian system, and equation (2) is the tracking error system of the spacecraft formation, where For the variable error of the port Hamiltonian system (1) in the generalized state, For the Hamiltonian function of the tracking error system, For error system input, For the error system output, where It is an antisymmetric matrix, representing the interconnection matrix of the tracking error system. It is a non-negative definite symmetric matrix, representing the damping matrix of the tracking error system.

[0082] Theorem 1: Consider the port Hamiltonian system (1). For any scalar function Q(x,t) and any vector function β(x,t), there exists a pair of functions Φ(x,t) and α(x,t) that produce a generalized regular transformation as shown in equation (2).

[0083] Functions Φ(x,t), Q(x,t), and β(x,t) produce generalized regular transformations if and only if there exists K(x,t) = -K(x,t). T S(x,t)=S(x,t) T R+S≥0, satisfying the partial differential equation:

[0084]

[0085] at this time,

[0086] Theorem 2: For a general port Hamiltonian system, a generalized canonical transformation is performed using Q(x,t) and β(x,t), where H+Q≥0. If the storage function H satisfies:

[0087]

[0088] Then the new input / output mapping It is unpowered.

[0089] If equation (4) is satisfied, and the function If positive definite, then the feedback control is:

[0090]

[0091] The system is asymptotically stable through feedback control, where C(x,t)≥εI>0; secondly, if the transition system is zero-state detectable, the feedback control can make the system uniformly asymptotically stable.

[0092] Theorem 3: For the system If the desired Hamiltonian function H can be found d (x), symmetric matrix R d (x)≥0 and antisymmetric matrix J d (x) satisfies the partial differential equation:

[0093]

[0094] In the formula g ⊥ (x)g(x)=0, and x * For H d The local minimum point of (x), This is a locally stable equilibrium point of the closed-loop system.

[0095] The control law for the port Hamiltonian system is:

[0096]

[0097] Transform the port Hamiltonian system into

[0098]

[0099] Additionally, if Included In the middle, and its closed-loop system (8) has a maximum invariant set equal to {x} * If the port Hamiltonian system is asymptotically stable, then the system is asymptotically stable.

[0100] This invention considers a formation of spacecraft in Earth orbit. Because the orbital elements of each spacecraft differ only slightly from those of a reference orbit, each spacecraft follows and moves in the vicinity of a reference point (real or virtual). If the reference orbit is circular, the motion of the center of mass of each spacecraft relative to the reference point can be approximated by the linear dynamic model of the (Clohessy-Wiltshire, CW) equations.

[0101] Its spacecraft dynamics model (after normalization) is as follows:

[0102]

[0103] In the formula: For spacecraft state variables, u = [u x ,u y ,u z ] T It is the control acceleration of the spacecraft, I is the identity matrix, and the coordinate system is the rotated Euler-Hill reference coordinate system.

[0104] To ensure that the spacecraft has a closed relative motion trajectory, take Let ω be the angular velocity, then the analytical solution to the CW equation is:

[0105]

[0106] In the formula:

[0107]

[0108]

[0109]

[0110] Where a is a unit of length, representing the size of the orbit; φ is a unit of angle, representing the position of the orbiting satellite in its orbit; and b is the magnitude of the vibration amplitude in the z-direction. Let x0 be an angle, and z0 be the vibration phase in the z-direction; x, z, Initial value.

[0111] Based on Definition 1 and Theorem 1, a generalized canonical transformation is applied to the spacecraft's relative motion trajectory tracking, yielding the Hamiltonian energy function of the spacecraft's relative motion:

[0112]

[0113] Therefore, combining equation (9), we can obtain the relative motion equation PH of the target spacecraft formation as follows:

[0114]

[0115] In the formula:

[0116]

[0117]

[0118]

[0119] In order to construct a tracking error system for the spacecraft PH system and ensure its stability, the generalized regularity proposed in Definition 1.1 is used to transform the relative motion PH equation.

[0120] Pick

[0121]

[0122] In the formula For the desired state of the spacecraft, we can obtain from equation (13):

[0123]

[0124]

[0125] Therefore, according to definition 1.1, the Hamiltonian energy function of the transformed tracking error system can be obtained from equations (11) and (13):

[0126]

[0127] From equation (16), we can obtain the following expression:

[0128]

[0129]

[0130] To obtain the state expression after the generalized regular transformation, equation (3) is solved, where K = 0. 6×6 , And from equation (12), we know that R = 0 and S = 0, therefore we can obtain:

[0131]

[0132] Therefore:

[0133] Based on Theorem 2, this embodiment of the invention performs stability analysis on the tracking error system obtained after performing a generalized canonical transformation on the relative motion equations PH of the target spacecraft formation. The process is as follows:

[0134] when

[0135] and hour,

[0136] Solving equation (4), we get:

[0137]

[0138] Therefore, it can be concluded that the tracking error system obtained after the generalized canonical transformation is a passive system.

[0139] make From equation (2) and It can be seen that when From time to time

[0140]

[0141] as well as

[0142]

[0143] From equations (23) and (24), we can obtain Therefore, it can be concluded that the tracking error system can be detected in the zero state.

[0144] Therefore, according to Theorem 2, there exists a feedback control (5) that makes the tracking error system uniformly asymptotically stable.

[0145] Specifically, in this embodiment of the invention, a distributed control law for formation trajectory tracking that considers the relative error between adjacent spacecraft is derived using Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). The specific process is as follows:

[0146] A graph consisting of a given set of nodes and edges connecting any two nodes can be represented as G = (V, E, A), where V = (v1, v2, ..., v...). n (v) is a finite, non-empty set of nodes, and the edge set E = V × V is a set of unordered pairs of distinct nodes. i ,v j )∈E is node v i and v j For adjacent nodes, node v i and v j Information can be obtained from each other, and let node v be a record. i The neighbor set is V i ={v j ∈V:(v i ,v j )∈E}. Adjacency matrix A=[a ij ]∈R n×n Defined as: when (v i ,v j When )∈E, we have a ij =1, otherwise a ij =0. The values ​​of the elements of the Laplacian matrix L of the graph are as follows:

[0147]

[0148] Based on the characteristics of the PH system, that is, a system composed of multiple systems with PH structures is still a PH system, the Hamiltonian function of the formation tracking error system composed of multiple spacecraft tracking error systems can be obtained from equation (16):

[0149]

[0150] In the formula Let be the error Hamiltonian function of spacecraft i. Let be the state error of spacecraft i.

[0151] From equation (26), we can obtain:

[0152]

[0153] In the formula This refers to the status of the formation tracking error system.

[0154] Therefore, the PH equation for the tracking error system of the target spacecraft formation can be obtained as follows:

[0155]

[0156] in, For spacecraft velocity and acceleration errors, I n Let n be an n-order identity matrix, where n is the number of spacecraft. For the Kronecker product of matrices, For spacecraft interconnection matrix, Let Hamiltonian function be the tracking error system of a spacecraft formation, which consists of multiple spacecraft tracking error systems. For the formation tracking error system status, It is a coefficient matrix with no specific physical meaning. For formation error system output, This is the system control law.

[0157] Specifically, in order to maintain the relative motion configuration of the target spacecraft formation, this embodiment of the invention couples the relative position error between the spacecraft into the system, and takes the Hamiltonian expected Hamiltonian function of the tracking error system of the target spacecraft formation as:

[0158]

[0159] Where n is the number of spacecraft, a ij For elements of the adjacency matrix, a ij ≠0, k p For interconnection coefficients, The error in maintaining the relative distance between spacecraft i and spacecraft j. Let be the error of the i-th spacecraft. Let be the error of the j-th spacecraft.

[0160] Specifically, step 4 includes:

[0161] From equation (29), we can obtain:

[0162]

[0163] Solve the matching equation according to Theorem 3.

[0164]

[0165] Because G ⊥ G = 0 and G ⊥ Full rank, G can be selected. ⊥=[I3 0 3×3 ], and set

[0166]

[0167] Substituting equation (32) into equation (31) yields the following equation:

[0168]

[0169] in,

[0170] according to and The arbitrariness of J satisfies the condition of this equation. 11 =R 11 J 12 =I3. Therefore, we can assume

[0171]

[0172] In the formula k d is the damping coefficient.

[0173] According to Theorem 3, the control law for the target spacecraft formation is:

[0174]

[0175] Substituting equations (27), (30), and (34) into (35), the control law of the target spacecraft formation tracking error system can be obtained as follows:

[0176]

[0177] From equation (36), the control law for the i-th satellite in the tracking error system can be obtained as follows:

[0178]

[0179] From Definition 1 and Equation (37), the control law for the i-th satellite in the port Hamiltonian system is:

[0180]

[0181] In the formula A i =(a i1 ,a i2 ,…a in ),

[0182] This invention provides an embodiment of a stability analysis of the port Hamiltonian system of a target spacecraft formation, the process of which is as follows:

[0183] because and

[0184]

[0185] And because hour,

[0186] Therefore included The maximum invariant set of the closed-loop system in the equation is equal to According to Theorem 3, this closed-loop system is asymptotically stable.

[0187] The following embodiments of the present invention provide two specific simulation examples for spacecraft formation configuration control, one using a generalized regular transformation method and the other a passive control method based on graph theory and interconnected damping allocation. Example 1 is mainly used to verify the trajectory tracking control of the relative motion of two spacecraft (leader and follower); Example 2 is mainly used to verify the distributed maintenance control of the relative motion configuration of seven spacecraft in formation. The specific simulation process is as follows:

[0188] Assume the spacecraft is orbiting near a reference point in a near-Earth circular reference orbit at an altitude of 600 km. The semi-major axis of this reference point is 6978.173 km, the eccentricity is 0, the orbital inclination is π / 6, the right ascension of the ascending node is π / 3, and the argument of latitude is 0. Calculate the orbital angular velocity of the reference orbit as ω = 1.0831 × 10⁻⁶. -3 The simulation was performed using MATLAB's ODE45 function to solve the differential equations, with a step size of 0.1 s and a relative accuracy of 10 rad / s. -8 The absolute precision is set to 10. -9 .

[0189] In the simulation, the effects of nonlinearity and the J2 term perturbation due to the non-spherical shape of the Earth were considered. At each time step of the simulation calculation, the absolute motion state of each spacecraft in the geocentric inertial coordinate system was first transformed to the Euler-Hill coordinate system of the reference point. Then, based on the relative motion state in the Euler-Hill coordinate system, the proposed control law was applied to calculate the control acceleration of each spacecraft. The generated control acceleration was then transformed back to the geocentric inertial coordinate system, and the absolute motion state of the spacecraft in the next time step was obtained through numerical integration.

[0190] Example 1

[0191] The control law in equation (23) and the feedback control in equation (5) are adopted, where C = -0.5I. The initial relative position of the following spacecraft in the Euler-Hill coordinate system, which is the reference point of the leading spacecraft, is (0.866km, -1km, 0.848km), and the initial relative velocity is (-0.54155m / s, -1.9m / s, 0.57396m / s). The desired relative motion trajectory is determined by equation (13), where a = 1km, k = 1.01, φ = 30°. Based on the expected relative motion trajectory, it can be concluded that the tracking error between the follower spacecraft and the leader spacecraft tends to stabilize at 1300s, and the final configuration control accuracy reaches the centimeter level; the steady-state control acceleration is very small, thus achieving low fuel consumption.

[0192] Example 2

[0193] The seven spacecraft generate formation configurations in the XYZ plane of the Euler-Hill coordinate system as shown in Table 1. Taking three of the spacecraft as examples, the formation configurations are as follows: Figure 2 As shown, the seven spacecraft are required to maintain this formation configuration and fly stably on the desired relative motion trajectory, as shown in Table 1 below, where Δ = 0.1:

[0194] Table 1

[0195]

[0196] Simulations were performed on both independent and distributed control methods for each spacecraft. The distributed control method uses a fixed network topology, and its adjacency matrix is ​​as follows:

[0197]

[0198] Independent control uses control laws in Distributed control uses control laws Where the interconnection coefficient k p =0.2, damping coefficient k d =0.1. Initial orbital angles of each spacecraft. and expected perspective Other trajectory parameters are shown in Table 1, and the specific simulation results are as follows: Figure 3-8 As shown, all results are in the Euler-Hill coordinate system. Figure 3 and Figure 4As shown in the figure, the trajectory error curve of the first spacecraft independent control law is represented by a solid line, the trajectory error curve of the second spacecraft independent control law is represented by a dashed line, and the trajectory error curve of the third spacecraft independent control law is represented by discrete points. The trajectory error curve of the first spacecraft distributed control law is represented by a solid line, the trajectory error curve of the second spacecraft distributed control law is represented by a dashed line, and the trajectory error curve of the third spacecraft distributed control law is represented by discrete points. From the curve results, the trajectory error when using the distributed control law is relatively small, and the convergence speed is faster.

[0199] like Figure 5 and Figure 6 As shown in the figure, when each spacecraft is controlled independently, the relative trajectory error curve between the first and second spacecraft is represented by a solid line; the relative trajectory error curve between the second and third spacecraft is represented by a dashed line; and the relative trajectory error curve between the third and first spacecraft is represented by discrete points. When each spacecraft is controlled in a distributed manner, the relative trajectory error curve between the first and second spacecraft is represented by a solid line; the relative trajectory error curve between the second and third spacecraft is represented by a dashed line; and the relative trajectory error curve between the third and first spacecraft is represented by discrete points. The results show that when distributed control is used, the trajectory error between adjacent spacecraft is relatively small, and the convergence speed is faster. Therefore, it can be concluded that when a distributed control law is used during the tracking process, the configuration maintenance accuracy between spacecraft is higher, and the stability is better.

[0200] like Figure 7 and Figure 8 As shown in the figure, the acceleration curve applied by the first spacecraft when each spacecraft is independently controlled is represented by a solid line, the acceleration curve applied by the second spacecraft when each spacecraft is independently controlled is represented by a dashed line, and the acceleration curve applied by the third spacecraft when each spacecraft is independently controlled is represented by discrete points. When each spacecraft is under distributed control, the acceleration curve applied by the first spacecraft is represented by a solid line, the acceleration curve applied by the second spacecraft when each spacecraft is under distributed control is represented by a dashed line, and the acceleration curve applied by the third spacecraft when each spacecraft is under distributed control is represented by discrete points. From the results analysis, it can be seen that the acceleration applied by the system is smaller when distributed control is used. Therefore, it can be concluded that less fuel is required for spacecraft formation trajectory tracking control when distributed control is used.

[0201] This invention constructs a relative motion equation (PH) for a target spacecraft formation to describe the relative trajectory of each spacecraft. The relative motion equation (PH) is then converted into a relative trajectory tracking error equation (PH), resulting in a tracking error system for the target spacecraft formation to describe the tracking error of the relative trajectory. Based on this tracking error system, a desired Hamiltonian function is constructed that couples the relative position error of each spacecraft in the target spacecraft formation to the tracking error system. A control law for the target spacecraft formation is designed based on the desired Hamiltonian function, and the actual and desired states of the target spacecraft formation are substituted into the control law for calculation, yielding the value of the distributed cooperative control law for the target spacecraft formation. Distributed trajectory tracking control of the target spacecraft formation is then performed based on the value of the distributed cooperative control law. Under the action of the distributed cooperative control law designed in this invention, the spacecraft formation can accurately and quickly reach the desired trajectory and maintain its configuration, achieving distributed cooperative control of a networked spacecraft cluster. Compared to the independent following control law of the prior art, this method achieves higher configuration maintenance accuracy, faster convergence speed, smaller applied acceleration, and also reduces the relative distance error between spacecraft.

[0202] This invention also provides a distributed control device for spacecraft formation trajectory tracking, comprising:

[0203] The building module is used to construct the relative motion equations (PH) of the target spacecraft formation; the relative motion equations (PH) are used to describe the relative motion trajectory of each spacecraft.

[0204] The conversion module is used to convert the relative motion equation PH for each spacecraft separately to obtain the relative motion trajectory tracking error equation PH for the target spacecraft formation, thus obtaining the tracking error system of the target spacecraft formation; the relative motion trajectory tracking error equation PH is used to describe the tracking error of the relative motion trajectory;

[0205] The construction module is used to construct the desired Hamiltonian function that couples the relative position error of each spacecraft in the target spacecraft formation to the tracking error system, based on the tracking error system.

[0206] The calculation module is used to design the control law of the target spacecraft formation based on the desired Hamiltonian function, and to calculate the value of the distributed cooperative control law of the target spacecraft formation by substituting the actual state and desired state of the target spacecraft formation into the control law.

[0207] The control module is used to perform distributed control for trajectory tracking of the target spacecraft formation based on the value of the distributed cooperative control law.

[0208] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of the present invention. For details on their specific functions and technical effects, please refer to the method embodiments section, which will not be repeated here.

[0209] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of the embodiments of the present invention. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0210] This invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements a distributed control method for spacecraft formation trajectory tracking.

[0211] If an integrated module is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying the computer program code to a building device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0212] This invention also provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a distributed control method for spacecraft formation trajectory tracking.

[0213] The terminal device can be a desktop computer, laptop, handheld computer, server, server cluster, or cloud server, etc. This terminal device may include, but is not limited to, a processor and memory.

[0214] The processor referred to can be a Central Processing Unit (CPU), but it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0215] In some embodiments, the memory may be an internal storage unit of the terminal device, such as a hard drive or RAM. In other embodiments, the memory may be an external storage device of the terminal device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital Card (SD), or Flash Card. Furthermore, the memory may include both internal and external storage units of the terminal device. The memory is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the computer program. The memory can also be used to temporarily store data that has been output or will be output.

[0216] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of the present invention. For details on their specific functions and technical effects, please refer to the method embodiments section, which will not be repeated here.

[0217] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of the embodiments of the present invention. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0218] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A distributed control method for spacecraft formation trajectory tracking, characterized in that, include: Step 1: Construct the relative motion equations (PH) for each spacecraft in the target spacecraft formation; The relative motion equation PH is used to describe the relative motion trajectory of each spacecraft; Step 2: Transform the relative motion equation PH for each spacecraft to obtain the relative motion trajectory tracking error equation PH for the target spacecraft formation. The relative motion trajectory tracking error equation PH serves as the tracking error system for the target spacecraft formation. The relative motion trajectory tracking error PH equation is used to describe the tracking error of the relative motion trajectory; Step 3: Based on the tracking error system, construct an expected Hamiltonian function that couples the relative position errors of each spacecraft in the target spacecraft formation to the tracking error system. The expected Hamiltonian function is... : in, For the number of spacecraft, For adjacency matrix elements, , , For interconnection coefficients, For spacecraft With spacecraft The error in maintaining the relative distance between them , For the first i The error of a spacecraft For the first j Errors of individual spacecraft; Step 4: Design the control law of the target spacecraft formation based on the desired Hamiltonian function, and substitute the actual state and desired state of the target spacecraft formation into the control law for calculation to obtain the value of the distributed cooperative control law of the target spacecraft formation; Step 5: Perform distributed trajectory tracking control on the target spacecraft formation based on the value of the distributed cooperative control law.

2. The distributed control method for spacecraft formation trajectory tracking according to claim 1, characterized in that, The relative motion equation PH for each of the spacecraft is: in, yes The derivatives of are the spacecraft velocity and acceleration. For the interconnection matrix of spacecraft, , , , , Let be the energy function. For the spacecraft's state variables, For time, It has no specific physical meaning. , For the input of the spacecraft, It is the identity matrix. For the output of spacecraft.

3. The distributed control method for spacecraft formation trajectory tracking according to claim 2, characterized in that, The equation for the relative motion trajectory tracking error PH of the target spacecraft formation is: in, For spacecraft velocity error and acceleration error, It is an n-order identity matrix. For the number of spacecraft, For the Kronecker product of matrices, For spacecraft interconnection matrix, Let Hamiltonian function be the tracking error system of a spacecraft formation, which consists of multiple spacecraft tracking error systems. For the formation tracking error system status, It is a coefficient matrix with no specific physical meaning. For formation error system output, This is the system control law.

4. The distributed control method for spacecraft formation trajectory tracking according to claim 3, characterized in that, Step 4 includes: Based on the Hamiltonian function of a spacecraft formation tracking error system composed of multiple spacecraft tracking error systems. We can obtain: in, State of the formation error system; The expected Hamiltonian function of the relative position error in the distributed topology is: According to if The expected Hamiltonian function in the system Symmetric matrix and antisymmetric matrix The theorem for partial differential equations holds, and the matching equation can be solved as follows: in, , For Laplace matrix, It is an adjacency matrix. , For matrix elements, , ; according to and The arbitrariness of , the condition for satisfying this equation is . , , can be set According to If the system expects the Hamiltonian function... Symmetric matrix and antisymmetric matrix Based on the theorem that satisfies partial differential equations, the control law for the target spacecraft formation is designed as follows: Will , , , Substitution In the process, the distributed cooperative control law of the target spacecraft formation is obtained as follows: in, is the damping coefficient.

5. The distributed control method for spacecraft formation trajectory tracking according to claim 4, characterized in that, Based on the distributed cooperative control law of the target spacecraft formation, the first [missing information] in the tracking error system of the target spacecraft formation can be obtained. The control law for each spacecraft is: According to the tracking error system, the first The control law of the target spacecraft formation can be obtained from the control law of the target spacecraft formation. The control law for each spacecraft is: in, .

6. A distributed control device for spacecraft formation trajectory tracking, characterized in that, include: The building module is used to construct the relative motion equations (PH) for each spacecraft in the target spacecraft formation; The relative motion equation PH is used to describe the relative motion trajectory of each spacecraft; The conversion module is used to convert the relative motion PH equation of each spacecraft to obtain the relative motion trajectory tracking error PH equation of the target spacecraft formation. The relative motion trajectory tracking error PH equation serves as the tracking error system of the target spacecraft formation. The relative motion trajectory tracking error PH equation is used to describe the tracking error of the relative motion trajectory; A construction module is used to construct, based on the tracking error system, an expected Hamiltonian function that couples the relative position errors of each spacecraft in the target spacecraft formation to the tracking error system, wherein the expected Hamiltonian function is: : in, For the number of spacecraft, For adjacency matrix elements, , , For interconnection coefficients, For spacecraft With spacecraft The error in maintaining the relative distance between them , For the first i The error of a spacecraft For the first j Errors of individual spacecraft; The calculation module is used to design the control law of the target spacecraft formation based on the desired Hamiltonian function, and to substitute the actual state and desired state of the target spacecraft formation into the control law for calculation to obtain the value of the distributed cooperative control law of the target spacecraft formation; The control module is used to perform distributed trajectory tracking control on the target spacecraft formation based on the value of the distributed cooperative control law.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the spacecraft formation trajectory tracking distributed control method as described in any one of claims 1 to 5.

8. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the spacecraft formation trajectory tracking distributed control method as described in any one of claims 1 to 5.

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